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Thank you for participating in the Grand Prix challenges last week!
Next week's challenge will be posted during @NicoleJohnson's Inspire Europe Weekly Challenge (10:30AM on Wednesday 10/10)! Finally, those on GMT challengers will finally have first crack at the challenge. Unless @patrick_digan wakes up at 5:30AM Eastern.
Onto this week's challenge!
There are 1000 lockers in a high school with 1000 students. The problem begins with the first student opening all 1000 lockers; the second student closes lockers 2,4,6,8,10 and so on to locker 1000; the third student changes the state (opens lockers closed, closes lockers open) on lockers 3,6,9,12,15 and so on; the fourth student changes the state of lockers 4,8,12,16 and so on. This goes on until
every student has had a turn.
When all 1,000 students have finished, which locker doors are open?
Ok, all you Math gurus. Can anyone explain why, iteratively applying the sieve of Eratosthenes, should generate that particular, very familiar, sequence of numbers? Is all of math beautifully connected at a level just below what common folk like me can see?
And what's up with Euler's Identity anyway